If x=1 is the vertical asymptote and y=-3 is the horizontal asymptote for the graph of the function f
which of the following could be the equation of the curve

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  1. The answer is D but can someone explain to me why it is?

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  2. x=1 is the vertical asymptote
    so you need a fraction with (x-1) in the denominator
    since division by zero is undefined, and if the numerator is not zero, there will be a vertical asymptote there.

    and y=-3 is the horizontal asymptote
    Since there is a horizontal asymptote, the degree of the numerator is equal to that of the denominator.
    Since the asymptote is at y = -3, the ratio of the leading coefficients is -3.
    So, an easy function would be 3(x-k)/(x-1) where k≠1
    That is not one of the choices, but D is the only choice which has the required factors.

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